Short-wave dynamics in the Euler equations

A new nonlinear equation governing asymptotic dynamics of short surface wav es is derived by using a short-wave perturbative expansion in an appropriat e reduction of the Euler equations. This reduction corresponds to a Green-N aghdi-type equation with a cinematic discontinuity in the surface. The phys ical system under consideration is an ideal fluid (inviscid, incompressible and without surface tension) in which takes place a steady surface motion. An ideal surface wind on a lake which produces surface flow is a physical environment conducive to the above-mentioned phenomenon. The equation obtai ned admits peakon solutions with amplitude, velocity and width in interrela tion.